Line a: slope -1, equation y = -x + 5. Line b: slope 0, equation y = -2.
The image you sent shows a graph with two lines labeled "a" and "b". The question asks us to identify the slope and equation of each line.
Line a:
To find the slope of line a, we can use the following formula:
m = (y₂ - y₁)/(x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are any two points on the line.
Let's choose the points (3, -2) and (6, -5). Plugging these values into the formula, we get:
m = (-5 - (-2))/(6 - 3) = -3/3 = -1
Therefore, the slope of line a is -1.
To find the equation of line a, we can use the following point-slope form:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a known point on the line and m is the slope of the line.
Plugging in the point (3, -2) and the slope -1, we get:
y - (-2) = -1(x - 3)
Simplifying, we get the equation:
y = -x + 5
Therefore, the equation of line a is y = -x + 5.
Line b:
Since line b is parallel to the x-axis, its slope is 0
To find the equation of line b, we can use the following point-slope form:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a known point on the line and m is the slope of the line.
Plugging in the point (3, -2) and the slope 0, we get:
y - (-2) = 0(x - 3)
Simplifying, we get the equation:
y = -2
Therefore, the equation of line b is y = -2